drawing a belt around a gear
A constrained shape like a belt or chain on a complex path can be generated using softbodies.



This solution is similar to "attract part of a mesh around an arc"



Procedure (tested on Blender 2.79)


Create geometry for the upper gear, lower gear, right guide, left guide, and belt. Make sure the gear geometry is inside the belt geometry and the guides are outside. This is important because collision between the objects will be used to shape the belt.





Set the top gears a guides as collision objects.





Set the belt as a softbody. Follow the setting below. The changes to setting are to get the belt to smoothly follow the forces applies. This is done by applying a large aerodynamic force to slow down the movement of the belt as it collides.





Animate the movement of the gears and guides to their final position. To fit the belt to the path from these parts, they need to move relatively slowly from their initial position to the final position. 
Run the animation and the belt will be stretched to follow the part shapes. (Note: A modifier was added to make the belt appear thicker) The final geometry can be applied following this method - "Saving the deformation"






A blend file for this is available at